Surface, Density, and Temperature Effects on the Water Diffusion and

Article Cite This: J. Phys. Chem. C 2018, 122, 6684−6690

pubs.acs.org/JPCC

Surface, Density, and Temperature Effects on the Water Diffusion and Structure Inside Narrow Nanotubes Mateus Henrique Köhler*,† and José Rafael Bordin*,‡ †

Instituto de Fı ́sica, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Brazil Campus Caçapava do Sul, Universidade Federal do Pampa, 96570-000 Caçapava do Sul, Brazil

J. Phys. Chem. C 2018.122:6684-6690. Downloaded from pubs.acs.org by DURHAM UNIV on 09/03/18. For personal use only.

‡

ABSTRACT: The nanoconfinement of water leads to outstanding anomalous behaviors. The interfacial interactions between water and surface is an important effect in the majority of these events. In this study, we have used the molecular dynamics simulations to investigate the diffusion characteristics of water molecules confined in narrow nanotubes with variable polarity. The nanotubes were built with hydrophilic or hydrophobic sites. Our results shows that there is a strong relation between density and surface properties for the water structuration inside the nanotubes. At low densities and narrower nanotubes, the surface characteristics play a major role, whereas for wider nanotubes, we observe distinct structuration at higher densities. The density is found to profoundly affect the water mobility in both nanotube species. This effect is accompanied by an organization in layers, resulting in structural transitions of water inside the nanotube as we increase the density. The temperature plays an important role in the transport of water inside small nanotubes. Our findings show that a small change in the nanotube diameter can lead to distinct dependence of diffusion with the temperature. The results indicate how density, temperature, and surface properties affect the dynamical and structural behavior of water inside narrow nanopores.

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INTRODUCTION Water, this extraordinary liquid, holds great fascination among scientists and curious people in general intrigued with its anomalies.1,2 Although we usually think in bulk water, it is eventually found confined in nature. For instance, the mass transportation among our cells is directly mediated by water flow in nanostructured channels (e.g., aquaporins3). A fascinating event takes place also when water enters the hollow cavity of a carbon nanotube (CNT), presenting what we call the superflux, exceeding the flow predicted by the continuum hydrodynamic theory by more then 3 orders of magnitude.4 This phenomenon has been widely investigated in the last decade. However, some questions still pose as open subjects. The atomically smooth surface and ordered molecular structure make the CNT an energy-efficient escape for the water molecules. The water’s journey through a nanotube is full of anomalous structural and dynamical behaviors, making these systems interesting models for biomolecular mass transportation studies and for potential new technologies. In recent years, a number of computational and experimental studies have been conducted to understand the water flow through hydrophobic,5 modified,6 and charged7 narrow channels. The possibility of tuning the water−CNT interaction, by making it more hydrophilic or hydrophobic, is important either to achieve higher water permeation or to induce it to experience structural and dynamical transitions. The impact of © 2018 American Chemical Society

hydrophobicity over water properties has aroused long debate. Chemically functionalized nanotubes8−10 and biological molecules11,12 can show hydrophobic and hydrophilic sites. This adds even more complexity to this picture and presents an opportunity to study the effect of polarity heterogeneity over confined water properties. As we increase the degree of confinement by decreasing the nanotube radius, the hydrophobic effect over the water properties is expected to be more pronounced because the nanotube−water interactions becomes more frequent than the water−water interaction. In fact, Hummer and colleagues13 have demonstrated that a small change in the water−carbon interaction strength can profoundly impact the water occupancy inside small CNTs. Moskowitz et al.14 have found that the water flux through nanotubes is sensitive to the fraction of hydrophobic/hydrophilic atoms, regardless of their arrangement. It is intriguing, however, that when located in the tube entrance, the hydrophobic atoms can play some role, lowering the filling rate.15 Additionally, Xu and his group16 found a maximal flow when empty states are present in the inner of the nanotube, which is unexpected because in this situation the wired hydrogen-bonding network (prerequisite for high water Received: January 4, 2018 Revised: February 8, 2018 Published: March 8, 2018 6684

DOI: 10.1021/acs.jpcc.8b00112 J. Phys. Chem. C 2018, 122, 6684−6690

Article

The Journal of Physical Chemistry C

the diffusion regime: α = 1 for linear Fickian diffusion, α > 1 for superdiffusive and α < 1 for subdiffusive regime. In the bulk phase, the water molecules diffuse as the Fickian type. However, with water confined in CNTs, the diffusion behavior becomes extraordinary due to the nanoscale confinement.26 For a fluid, the statistical error could be reduced by averaging over all the MSD components. But the nanopore confinement in the x- and y-directions hinders the radial displacement of the molecules. Therefore, the radial MSD is almost 0 for all cases studied here and only the axial MSD will be considered. We use the effective diameter deff = d − σCO,33 where d is the nominal diameter and σCO is the Lennard-Jones (LJ) parameter for carbon−oxygen interaction, to calculate the water density inside the nanotube. In terms of deff, the effective density is then given by

permeability) is broken. All these results point out that there are still important parameters to be taken into account in the general physical−chemical understanding of the properties of confined water, especially regarding the nanopore polarity. Another affecting parameter is the temperature. The distinct behavior of confined and bulk water leads to distinct freezing temperatures and regions of liquid−ice coexistence.17,18 For instance, experimental and computational studies indicates that water can freeze inside CNTs at high temperatures, where bulk water is in boiling conditions.19,20 In this way, in this paper, we employ molecular dynamics to analyze the impact of hydrophobic or hydrophilic surface and distinct temperatures over the structure and dynamics of the water confined inside small nanotubes. The diffusion behavior and the molecular distribution of the confined water were analyzed for nanotubes with diameters ranging from 0.8 to 1.1 nm. The paper is organized as follows. In the next section, Computational Details and Methods are described. In Results and Discussion, the main results of the dynamic and structural properties of the confined water are discussed. Summary and Conclusions are presented in last section.

ρeff =

π ·S·

deff 2 2

( )

(2)

where M is the total water mass into the pore and S is the nanotube length. In Figure 1, we present a depiction of the

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COMPUTATIONAL DETAILS AND METHODS Water and Nanotube Models. Molecular dynamics were performed using the LAMMPS package21 for simulations of TIP4P/2005 water22 confined inside nanotubes. The choice of TIP4P/2005 over many other models available in the literature was due to its accuracy in calculating the transport properties of water at ambient conditions.22,23 Particularly for the bulk diffusion coefficient, we have found 2.32 × 10−9 m2/s, which is in close agreement to previous theoretical24 and experimental works.25 The nanotube atoms are arranged on a honeycomb lattice. Two different atom types were used to build the nanotube. They differ only by their Lennard-Jones (LJ) parameters of interaction with water and correspond to sp2hybridized carbon with εCO = 0.478 kJ/mol and σCO = 0.328 nm (labeled hydrophilic due to water attractive character) and reduced carbon−water interaction strength with εCO = 0.27 kJ/ mol and σCO = 0.341 nm (namely hydrophobic), as done in previous works.13,26,27 We considered three cases of (n,n) nanotubes, with n = 6, 7, and 8. Periodic boundary conditions were applied to simulate isolated infinite nanotubes. The cutoff distances for LJ and Coulomb interactions are 1.0 and 1.2 nm, respectively. Longrange Coulomb interactions was handled using particle− particle particle−mesh method.28 The simulations were conducted in the NVT ensemble at temperature 300 K fixed by a Nosé−Hoover thermostat.29,30 Each nanotube was filled up to the desired density for each combination of ε and temperature. The system was then equilibrated with a 15 ns simulation, followed by 15 ns of data accumulation. The timestep is 1 fs. In all simulations, the geometry of water molecules was constrained by the SHAKE algorithm.31 For each case, three independent simulations were performed. Simulation Details. The diffusion mechanism of a fluid can be reflected by the scaling behavior between the mean squared displacement (MSD) and time32 2 α ⟨| r (⃗ t ) − r (0) ⃗ | ⟩ ∝ Dt

M

Figure 1. Frontal and lateral snapshot of (a) and (b) (6,6), (c) and (d) (7,7), and (e) and (f) (8,8) nanotube filled with water. Red spheres stands for oxygen atoms, white for hydrogen, and the carbon atoms are colored as silver dynamic bonds.

Table 1. Nominal Diameter d, Length S , Number of Enclosed Molecules N, and the Range of Effective Densities (ρeff) for the Nanotube Samples chirality

d (nm)

S (nm)

N

ρeff (g/cm3)

(6,6) (7,7) (8,8)

0.81 0.95 1.08

205 102 60

750−1100 750−1050 650−1120

0.6−0.9 0.7−1.0 0.7−1.2

computational framework. In Table 1, the nanotube chirality, nominal diameter d, length S , number of enclosed water molecules N, and the considered effective densities ρeff are presented. The water radial density profile was evaluated by dividing the inner of the nanotube in concentric cylindrical shells and averaging the number of oxygen atoms in each shell along the simulation.

(1)

where ⟨|r(⃗ t) − r(⃗ 0)|2⟩ is referred as the MSD, ⟨⟩ denotes an average over all the molecules, and r(⃗ t) is the displacement of a molecule during the time interval t. The α exponent refers to 6685


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Figure 2. Two-dimensional color density maps of oxygen atoms inside (6,6) nanotubes and frontal snapshot of the final configuration for (a, b) 0.6 g/cm3 and (c, d) 0.9 g/cm3.

Figure 3. Radial density profile of oxygen atoms inside (6,6) nanotubes for densities (a) 0.6 g/cm3 and (b) 0.9 g/cm3.

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RESULTS AND DISCUSSION Surface Chemistry and Density Effect. Water structure and dynamics under hydrophobic and hydrophilic confinement is relevant to understand and develop new technologies, as well to understand aspects of life and basic science. For instance, nonpolar or weakly polar pores play a prominent role in aquaporin water channels.34 In such systems, water occupies their weakly polar pores at least transiently, exhibiting anomalous diffusion and dipoles aligned with the transmembrane axis. The pore polarity is therefore an important parameter in the confined water properties. To understand the behavior of water confined in hydrophobic and hydrophilic nanotubes at different densities, we first discuss the water molecules arrangement inside these structures. In Figure 2, we show the radial structuration of water molecules inside (6,6) nanotubes. At this small nanotube radius, the confinement induces a straight single-file of molecules and any physical parameter should affect the structure assumed by the water.35 For the lower density, Figure 2a, the water molecules tend to settle at the center of the tube. In this case, we can observe that the hydrophobic

confinement increases the accumulation of water molecules at the center compared with the hydrophilic case, Figure 2b. This difference is clear also in the density profile, Figure 3a. As the number of water molecules in the inner hole of the (6,6) nanotube increases, the arrangement changes to a zigzag single layer, with the molecules closer to the wall, as indicated by Figure 2c,d. At these higher densities, the nanotube polarity plays a small role, with both cases showing similar radial density maps. Figures 2 and 3 show that higher densities weakens the surface effect for (6,6) nanotubes, leading to similar radial distribution arrangement for both hydrophobic and hydrophilic confinements. The increase in the nanotube radius leads to distinct structures. In Figure 4, we show the radial structuration of water molecules inside a (8,8) nanotube. Here, for lower densities, we find that the water molecules form a square structure, as shown in Figure 4a. This layered arrangement is not affected by the pore polarity: the radial density map in Figure 4b for hydrophobic nanopores is essentially the same as that for the hydrophobic case, as the snapshot indicates. Also, the density profile, Figure 5a, reinforces this finding. At higher 6686


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Figure 4. Two-dimensional color density maps of oxygen atoms inside (8,8) nanotubes and frontal snapshot of the final configuration for (a, b) 0.7 g/cm3 and (c, d) 1.2 g/cm3.

Figure 5. Radial density profile of oxygen atoms inside (8,8) nanotubes for densities (a) 0.7 g/cm3 and (b) 1.2 g/cm3.

regarding the nanotube surface properties, as shown in Figure 6b,c. The hydrophilic nanotubes have a higher mobility for the lower densities. Increasing the density of both species of nanotubes leads to the same slope in the MSD curve. We can associate this with the change in the conformation. For the lower density, the water has a tubular square structure, and the diffusion is affected only by the water−wall friction. On the other hand, at higher densities, we observed a tubular layer with a central single-file layer. Therefore, here we have the water− water friction as a new feature, which leads to both hydrophilic and hydrophobic nanotubes to have the same diffusive behavior.9,26 Role of Temperature. The diffusion coefficient of water is known to be sensitive to temperature variations.39,40 In confined fluids, we can observe heterogeneous dynamics, which lead to anomalous diffusional behaviors.41,42 Nanotubes usually induce the confined water to present multiphase transitions at different temperatures.43,44 These structures are eventually connected with water mobility inside the pore, which generates a wide range of possibilities for controlling the fluid flow.

density, the water structure changes to a external pentagonal layer with a central single-file layer, as the Figure 4c,d show. Despite the apparent similarity in the snapshot and in the color map, for a higher density, there are small differences in the structure regarding the nanotube surface properties: the hydrophobic nanotube shows a slightly less water packing at the nanotube interface but allows a denser arrangement of molecules at the center. This is clear in the density profile of Figure 5b, where the peak near the center of the nanotube is higher for hydrophobic nanotubes, whereas the one near the wall is higher for hydrophilic nanotubes. Fluids structure and diffusion inside nanopores are strongly related.36−38 Therefore, distinct structural regimes can lead to different diffusive behaviors. In Figure 6, we present the MSD as a function of simulation time for the confined water. We can notice that the nanotube radii induces differences to the water’s diffusive behavior: whereas inside (7,7) and (8,8) nanotubes water undergoes Fickian diffusion (MSD ∝ t), in the smaller (6,6) nanotube, the water molecules present a transition from a initial ballistic diffusion (inset of Figure 6a) to a plateau, where a stationary state can be implied. The water at low density inside (7,7) and (8,8) nanotubes has distinct MSD slopes 6687


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Figure 7. Axial diffusion coefficient Dz as a function of temperature T for a system with density 0.9 g/cm3. The error bars stand for standard deviation from three independent simulations. The dotted lines are guide to the eyes based in polynomial fits, Dz = 6(T γ ). For the (7,7) nanotube, both curves can be fitted by the same line.

Figure 6. MSD versus time for (a) (6,6), (b) (7,7), and (c) (8,8) hydrophobic and hydrophilic nanotubes.

T = 450 K, the diffusion constant is approximately the same for (7,7) and (8,8) hydrophobic nanotubes. However, for the hydrophilic nanotubes, the diffusion inside the wider nanotube is small even at 450 K. As expected, the distinct dynamical features are correlated to distinct structural conformations. In Figure 8a, we show the oxygen’s radial density profile at different temperatures for (7,7) nanotubes. As the curves indicates, both hydrophilic and hydrophobic surfaces have almost the same structure, with the same radial position for the peaks for a given temperature. This shows why both surfaces lead to the same dependence of the diffusion coefficient. Remarkably, for 400 and 450 K, there is a slight difference in the peak’s magnitude between the hydrophobic and hydrophilic pores, which implies a slightly more organized water layer inside the latter nanotube. This explains why the axial diffusion above 400 K is smaller inside the hydrophobic (7,7) nanotubes: the more organized the water molecules are, less collisions occur between the water molecules, and the axial displacement is facilitated through the tube. On the other hand, for (8,8) nanotubes, Figure 8b, the unpacking of the water molecules close to the interface is more clear. By increasing T, the peak decreases and the distribution spreads toward the nanotube surface. Also, in all cases, the packing is more pronounced for hydrophilic surfaces, which means the water molecules are more structured. Therefore, the friction is lower and the diffusion is higher, as we have observed in Figure 7b. This shows how the structural and dynamical properties of water inside nanotubes with distinct surfaces depends on the pore diameter.

To clarify the effect of temperature over the dynamics of water confined in hydrophobic and hydrophilic nanotubes, we show in Figure 7 the diffusion of water molecules as a function of temperature. Because the water inside the (6,6) nanotube shows no mobility at 300 K, here we focused in the wider nanopores. As well, in these simulations, we have considered the case of density 0.9 g/cm3 because the MSD for hydrophilic and hydrophobic nanotubes have the same slope for (7,7) and (8,8) nanotubes, Figure 6b,c. At this density, the water has a tubular structure, without the central layer, which implies the water−wall interaction to be prominent. Therefore, we can relate changes in dynamics with the temperature and surface effects. For temperatures lower than 300 K, the diffusion coefficient is practically 0 at 275 K for (8,8) nanotubes and at 250 K inside (7,7) nanotubes. Because our goal is to study the diffusive properties, we show in Figure 7 the dependence of Dz on temperature, which ranges from 300 to 450 K. Despite the small difference in the diameter, 0.13 nm, a clear difference is noticeable in the diffusion inside each nanotube. For (7,7) nanotubes, the water have a higher mobility at 300 K than inside (8,8) nanotubes. This higher diffusion in narrower nanotubes near room temperatures was already reported in the literature.45,46 Above 300 K, the diffusion constant Dz shows a linear increase inside (7,7) nanotubes, i.e., Dz ∼ T. On the other hand, Dz grows with 6(T 3) for (8,8) nanotubes. Also, whereas for (7,7) nanotubes, Dz is approximately the same for hydrophobic and hydrophilic nanotubes up to 400 K, and slightly smaller above this threshold, for (8,8) nanotubes, all values obtained for Dz are higher inside the hydrophobic channels. Due to the distinct dependence with temperature, at

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SUMMARY AND CONCLUSIONS In this work, we have investigated through molecular dynamics simulations, the effect of hydrophobicity over the structure and 6688


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Figure 8. Oxygen’s radial density profile inside (a) (7,7) and (b) (8,8) nanotubes at distinct temperatures. Solid lines stands for hydrophilic surfaces, whereas dashed lines for hydrophobic nanotubes. (4) Majumder, M.; Chopra, N.; Andrews, R.; Hinds, B. J. Nanoscale hydrodynamics: Enhanced flow in carbon nanotubes. Nature 2005, 438, 44. (5) Secchi, E.; Marbach, S.; Nigues, A.; Stein, D.; Siria, A.; Bocquet, L. Massive radius-dependent flow slippage in carbon nanotubes. Nature 2016, 537, 210−213. (6) Giovambattista, N.; Almeida, A. B.; Alencar, A. M.; Buldyrev, S. V. Validation of capillarity theory at the nanometer scale by atomistic computer simulations of water droplets and bridges in contact with hydrophobic and hydrophilic surfaces. J. Phys. Chem. C 2016, 120, 1597−1608. (7) Khodabakhshi, M.; Moosavi, A. Unidirectional transport of water through an asymmetrically charged rotating carbon nanotube. J. Phys. Chem. C 2017, 121, 23649−23658. (8) Thomas, M.; Corry, B.; Hilder, T. A. What have we learnt about the mechanisms of rapid water transport,ion rejection and selectivity in nanopores from molecular simulation? Small 2014, 10, 1453−1465. (9) Bordin, J. R.; Barbosa, M. C. Flow and structure of fluids in functionalized nanopores. Phys. A 2017, 467, 137−147. (10) Setaro, A. Advanced carbon nanotubes functionalization. J. Phys.: Condens. Matter 2017, 29, No. 423003. (11) Köhler, M. H.; Barbosa, R. C.; da Silva, L. B.; Barbosa, M. C. Role of the hydrophobic and hydrophilic sites in the dynamic crossover of the protein-hydration water. Phys. A 2017, 468, 733−739. (12) Martelli, F.; Ko, H.-Y.; Borallo, C. C.; Franzese, G. Structural properties of water confined by phospholipid membranes. Front. Phys. 2018, 13, No. 136801. (13) Hummer, G.; Rasaiah, J. C.; Noworytra, J. P. Water conduction through the hydrophobic channel of a carbon nanotube. Nature 2001, 414, 188. (14) Moskowitz, I.; Snyder, M. A.; Mittal, J. Water transport through functionalized nanotubes with tunable hydrophobicity. J. Chem. Phys. 2014, 141, No. 18C532. (15) Ramazani, F.; Ebrahimi, F. Uncertainties in the capillary filling of heterogeneous water nanochannels. J. Phys. Chem. C 2016, 120, 12871−12878. (16) Xu, Y.; Tian, X.; Lv, M.; Deng, M.; He, B.; Xiu, P.; Tu, Y.; Zheng, Y. Effects of water-channel attractions on single-file water permeation through nanochannels. J. Phys. D: Appl. Phys. 2016, 49, No. 285302. (17) Moore, E. B.; Alle, J. T.; Molinero, V. Liquid-ice coexistence below the melting temperature for water confined in hydrophilic and hydrophobic nanopores. J. Phys. Chem. C 2012, 116, 7507−7514. (18) Giovambattista, N.; Rossky, P.; Debenedetti, P. Computational studies of pressure, temperature, and surface effects on the structure and thermodynamics of confined water. Annu. Rev. Phys. Chem. 2012, 63, 179−200. (19) Agrawal, K. V.; Shimizu, S.; Drahushuk, L. W.; Kilcoyne, D.; Strano, M. S. Observation of extreme phase transition temperatures of water confined inside isolated carbon nanotubes. Nat. Nanotechnol. 2017, 12, 267−273. (20) Pugliese, P.; Conde, M. M.; Rovere, M.; Gallo, P. Freezing temperatures, ice nanotubes structures, and proton ordering of

dynamics of water confined in small nanotubes. The results point that the influence of the water−wall interaction over its properties is dependent on temperature, density, and nanotube diameter. The structural and dynamical properties reported in the previous section all consistently show that the increase in density leads to a higher structuration for all the samples. The organization in layers is certainly preferred by the water molecules to decrease the bond enthalpy at the high-density regime, but at the cost of mobility. The temperature has been shown as a critical parameter for water mobility inside the nanotubes. Particularly, for higher temperatures, we have found different diffusion of water confined in hydrophilic (8,8) nanotubes compared with hydrophobic pores. Also, the dependence on the temperature is distinct for (7,7) and (8,8) nanotubes. This variation is also accompanied by changes in the water organization inside each nanotube. These findings shed some light on heterogeneous nanofluidics and are helpful in understanding the distinct behavior of water near polar and apolar sites in functionalized synthetic nanopores and biological transmembrane channels.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (M.H.K.). *E-mail: [email protected] (J.R.B.). ORCID

Mateus Henrique Köhler: 0000-0001-9733-9630 José Rafael Bordin: 0000-0002-8025-6529 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge Brazilian science agencies FAPERGS, CNPq, and INCT-Fcx for financial support, CENAPAD-SP and CESUP-UFRGS for the computer time.

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Surface, Density, and Temperature Effects on the Water Diffusion and

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